Your home folder is the one named "harrybriels", and won't be named "home", unless that is actually the name of your user account. It's also identified by the icon that looks like a house.
I would suggest NOT dragging all those year-named files to your harrybriels folder. Make a new folder just for this one-time purpose (leave it on your desktop while you are deciding what to do with all those folders), so you don't suddenly have to look at hundreds of files in your own user folder.
The quickest way to clear off your desktop is to open the Desktop folder (should be in a finder sidebar, with that name "Desktop". Choose that folder, then, if needed, change to "List View". Then sort the file list by file name. Now it will be an easy task to drag all of the year-named folders to another folder. Again, I would make one just for this purpose. That will clear off ALL of those year-named folders from your desktop.
BUT, I would be curious what exactly is in those folders (open one or two randomly), and WHY there are hundreds of those folders named from 15 or more years ago. My guess is those were created by some software that you were using years ago, maybe something used for file backups.
Do the files in those folders look familiar to you at all?
If there is nothing that looks remotely interesting -- after 15 years, you can probably drag that packed folder to the trash (don't forget to empty the trash to clear up the space on your drive!)